Ciphers of the Monks

Astrolabe marked with the ciphers

Read more...In addition to the Roman and Arabic numerals, there was another long-lived style of numeration in Europe, which is barely known today. It is described in a beautiful book The Ciphers of the Monks: A Forgotten Number-notation of the Middle Ages by David A. King.

The Basingstoke Cipher

Matthew Paris:

"Master J(ohn of Basingstoke) had informed Archbishop Robert of Lincoln that when he studied in Athens, he had seen and studied under the most learned of the Greek scholars, who are unknown to the Latins. ... ... This Master J[ohn] then brought to England the numerals of the Greeks, figures which also serve to express the letters and the knowledge of their meaning, and made them known to his friends. Regarding these numerals, which we want to reproduce on this page, what is the most admirable and what we do not find in the case of the Roman or the Hindu-Arabic numerals (quod non est in Latino, vel Algorismo), is that any numer may be represented as one single figure. Trace a (vertical) line and draw lines going out from it and making with it a right, acute or obtuse angle, in the following manner." [Chap 2.2 p.51]
He also noted that "the worthiest of all these figures" was 55, being in the shape of the cross , and that the arrow-shaped cipher represented 33, the age of Jesus at his death.[pp.55]

The Cisternian Cipher

The Cisternian variety is described in Agrippa's Occult Philosophy Chap. xix. as "certain other notes of Magicians" which he "found in two most ancient books of Astrologers, and Magicians, certain most elegant marks of numbers, which [he] thought good to set down in this place."

It seems to me like close relative of the notation is found in Chap. xvii.

Variant Ciphers

A simpler 5-based family of variants are found in runic calendars, and the same logical progression of these numerals are found in the Ogham scales.


Quantum Mechanics, Haldane, and Leibniz

N. Wiener
Philosophy of Science Vol. 1, No. 4 (Oct., 1934) pp. 479-482

Dear Sir:
There has recently appeared in this journal a very interesting paper by Professor J.B.S. Haldane, entitled, "Quantum Mechanics as a Basis for Philosophy." [Philosophy of Science I, 78-79, 1934.] The paper might indeed be called, "Leibniz as a basis for Quantum Mechanics." The name of Leibniz does not occur once in the article, yet it is permeated with his spirit, and is just such a document as an orthodox Leibnizian might write should he be confronted with the development of mathematics and experimental science in the two centuries since the death of the master.
It may seem a gross anachronism to speak of Leibniz and of quantum mechanics in one breath, but this anachronism disappears when we reflect on the historical background of Leibniz. Our classical phyics, the physics of our fathers and our text-books, is dominated by Newton and his dynamics of particles. We had come to regard this science as physics par excellence, and to demand a mechanical model for our optics, electrical theory, etc. This dictatorship of mechanics has only given way to a more democratic rule in the physics of our present generation. Thus we are inclinded to forget that this dictatorship is not coeval with physics itself, and that there were heros before Newton. Among the pre-Newtonian physicists was Huyghens, the prophet of wave optics and the master of Leibniz qua physicist.
The present state of physics represents a Hegelian synthesis between Newton's thesis of particle and Huyghens' antithesis of wave. Modern optics supplants the pure wave theory of Clerk-Maxwell by a theory in which the particle aspects of light are more strongly emphasized. In the field of mechanics, on the other hand, the well-intrenched particle theory has been superseded by one recognizing the wave aspects of matter. For the first time since Newton, wave and particle, field theory and a theory of collisions, share all branches of physics more or less evenly.
It is traditional to represent Leibniz' theory of monads as a pluralistic spiritualism. If we divest Leibniz' language of its protective layer of orthodox Christian phraseology, we shall see it might as well be called a pluralistic materialism. Only a small part of the monads are souls, the greater part being naked monads gifted with apperception rather than perception or consciousness. They mirror the universe, but do not integrate this activity of mirroring into a self-conscious consciousness. This mirroring is best to be understood as a parallelism, incomplete it is true, between the inner organization of the monad, and the organziation of the world as a whole. The structure of the microcosm runs parallel to that of the macrocosm.
In modern quantum theory, the electron or similar particle is a microcosm. It carries with it a set of proper coordinates embracing the entire universe. In terms of these coordinates we may express everything happening everywhere and "everywhen", but the picture we thus obtain is blurred because of our ignoration of the proper coordinates pertaining to all other particles, and we have no unique way, as far as physics has gone at present, of translating statements concerning the microcosm into statements concerning the macrocosm. The more organized a system of elementary particles is, the less "naked" its electrons and constituent elements, the better it mirrors the universe, and the better can we read back from our partial system to the universe at large.
Haldane assimilates the living organisms of the world to the particles of physics. He reduces the apparent randomness of their action to the indeterminacy of quantum theory and the ability which they show to make a choice on the basis of a representation of the future, to the ability of an electron to cross a potential barrier because of a lower potential on the other side of that barrier. In other words, although Haldane calls his system a materialism, and jsut because he calls it a materialism he reduces the living organism and the soul to something of the same nature as the proton or electron. I can see no essential difference between the materialism which includes soul as a complicated type of material particle and a spiritualism which includes material particles as a primitive type of soul.
With all these similarities between Haldane and Leibniz, there are important differences which cast a curious light on the changes both of physical and biological science since Leibniz' time. Haldane and Leibniz treat the problem of individuality somewhat differently. For Leibniz the monad is a completely closed entity over all eternity. It may rise to the rank of a soul or be degraded to that of a naked monad, but it never loses its identity or fuses it with that of another monad. On the other hand in deference to the exigencies of modern biology and modern physics, Haldane does not make the individual identity of his particles or living being absolute. The electrons of present-day physics do not retain a traceable identity after a collision, nor is it possible to trace the identity of a living organism back to the conjugation of germ cells in which it has its origin. These two types of indeterminate identitiy known to modern science, are identified by Haldane in an extremely interesting speculation. On the other hand, at the time of Leibniz, neither problem had arisen. No one doubted that the identity of two particles could be traced beyond their collision and the prevailing spermatist theory of heredity and conception made the individual find its sole origin in a single spermatozoon, to which at that time was supposed to have an existence continuable back to the Creation. Nevertheless, Leibniz' great principle of the identity of indiscernibles, to which he appeals in connection with the perfect individuality of the monad, is retained in the modern view. Since we may permute two electrons in such a way that they will be indiscernible from each other, we now say that two electrons cannot have complete separable individualities, but must be no more than two aspects of a complex containing two or more electrons. The modern philosopher is more subtle than Leibniz in distinguishing between a unity of indiscernibility and a multiplicity arrived at by counting. This unity in plurality is perfectly familiar to the mathematician: for example, the Möbius strip is locally endowed with distinguishable sides, but as a whole has only one side.
The other important issue on which Haldane and Leibniz take opposite sides concerns the nature of causality. With Leibniz, causality is still an unbroken chain, with no place for chance, while Haldane takes the modern standpoint according to which chance is a category prior to causality. It is thus all the more remarkable that the Leibnizian principle of sufficient reason is a direct ancestor of the mathematical methods of quantum mechanics. The principle of sufficient reason asserts that this world differs from the other possible self-consistent worlds by embodying some greatest perfection -- in other words, by satisfying some principle of minimization. This must have been suggested to Leibniz by his knowledge of optics and his acquintance with the principle of Fermat, in accordance with which rays of light minimize the time of passage between two near points. Leibniz calls this principle the principle of optimism, and in this form it may readily serve as a basis for a rather fatuous contentment with the world as it is. Voltaire ridiculed this contentment on the part of the Leibnizian Maupertuis, but the fact remains that Maupertuis' application of Leibnizian method to the expression of the laws of Newtonian mechanics as the minimization principle of least action, has proved to be anything but fatuous. It must always be considered as a mark of the greatness of Leibniz, that his idea of representing the laws of physics by principles of minimization is the source of the mechanics of Lagrange and Hamilton, from whom the line of inheritance to Heisenberg and Schrödinger is clear and direct.
Again, Leibniz may be regarded as the forerunner of field theory. For Leibniz, the world is a plenum, and there is no action at a distance. A monad can only mirror a distant monad through the intervention of intermediate monads. Thus Leibnizian physics only awaits the introduction of the partial derivative to become a field physics. This step is taken in the writings of Leibniz' immediate disciples, the Bernoullis.
Leibniz clairvoyance into the future is explicable only on the basis of his universal information, universal interests, and universal genius. It is scarcely an accident that a scholar of the broad knowledge and interests of Professor Haldane takes up what is essentially a Leibnizian position. A philosophy with sufficient vvitality to appeal to first rate scholars two centuries apart is surely worth more consideration than that generally granted to it by the intellectual public.

N. Wiener
Department of Mathematics, Massachusettes Institute of Technology, Cambridge, Mass.


An excerpt about water

The Aztec god Tlaloc, Lord of all Sources of Water

What in water did Bloom, waterlover, drawer of water, watercarrier, returning to the range, admire?

Its universality: its democratic equality and constancy to its nature in seeking its own level: its vastness in the ocean of Mercator's projection: its unplumbed profundity in the Sundam trench of the Pacific exceeding 8000 fathoms: the restlessness of its waves and surface particles visiting in turn all points of its seaboard: the independence of its units: the variability of states of sea: its hydrostatic quiescence in calm: its hydrokinetic turgidity in neap and spring tides: its subsidence after devastation: its sterility in the circumpolar icecaps, arctic and antarctic: its climatic and commercial significance: its preponderance of 3 to 1 over the dry land of the globe: its indisputable hegemony extending in square leagues over all the region below the subequatorial tropic of Capricorn: the multisecular stability of its primeval basin: its luteofulvous bed: its capacity to dissolve and hold in solution all soluble substances including millions of tons of the most precious metals: its slow erosions of peninsulas and islands, its persistent formation of homothetic islands, peninsulas and downwardtending promontories: its alluvial deposits: its weight and volume and density: its imperturbability in lagoons and highland tarns: its gradation of colours in the torrid and temperate and frigid zones: its vehicular ramifications in continental lakecontained streams and confluent oceanflowing rivers with their tributaries and transoceanic currents, gulfstream, north and south equatorial courses: its violence in seaquakes, waterspouts, Artesian wells, eruptions, torrents, eddies, freshets, spates, groundswells, watersheds, waterpartings, geysers, cataracts, whirlpools, maelstroms, inundations, deluges, cloudbursts: its vast circumterrestrial ahorizontal curve: its secrecy in springs and latent humidity, revealed by rhabdomantic or hygrometric instruments and exemplified by the well by the hole in the wall at Ashtown gate, saturation of air, distillation of dew: the simplicity of its composition, two constituent parts of hydrogen with one constituent part of oxygen: its healing virtues: its buoyancy in the waters of the Dead Sea: its persevering penetrativeness in runnels, gullies, inadequate dams, leaks on shipboard: its properties for cleansing, quenching thirst and fire, nourishing vegetation: its infallibility as paradigm and paragon: its metamorphoses as vapour, mist, cloud, rain, sleet, snow, hail: its strength in rigid hydrants: its variety of forms in loughs and bays and gulfs and bights and guts and lagoons and atolls and archipelagos and sounds and fjords and minches and tidal estuaries and arms of sea: its solidity in glaciers, icebergs, icefloes: its docility in working hydraulic millwheels, turbines, dynamos, electric power stations, bleachworks, tanneries, scutchmills: its utility in canals, rivers, if navigable, floating and graving docks: its potentiality derivable from harnessed tides or watercourses falling from level to level: its submarine fauna and flora (anacoustic, photophobe), numerically, if not literally, the inhabitants of the globe: its ubiquity as constituting 90 percent of the human body: the noxiousness of its effluvia in lacustrine marshes, pestilential fens, faded flowerwater, stagnant pools in the waning moon.

-- James Joyce, Ulysses


A Tractat by William Parke

Universal Panacaea

Published by William Parke, Hermetick Philos. and Physitian.
In him was life, and the Life was the light of men; and the light shineth in darkness, and the darkness comprehendeth it not, John 1.4,5.
Printed in the Year, 1665.
To them that are Elected of God, and Born of Nature.


1. God is Unity in Trinity, and Trinity in Unity.
2. God is all things possible and existent.
3. All things are in God, as Rays in their Centre.
4. The reflection of Gods Image, in speculo trinitatis, was the beginning of the creation.

Axiomata of the Creation and Harmony of the World.

1. The image emanating from God, is the first matter of all things: The first termination whereof constituted the Circle of Intelligence; The second termination whereof constituted the Circle of Souls; The third termination whereof constituted the Circle of Nature; The fourth termination whereof constituted the Circle of Metals.
2. By the Reflection, each Circle was impregnated according to their distance from their Centre: viz. The Circle of Intelligence with Forms; The Circle of Souls with Ideas; The Circle of Nature with the Seminal Reasons; The Circle of Matter with Material Forms.
3. These Circles being Univocal and Homogeneous, are linked together by the Golden Chain of Unity, Love, and Harmony: viz. The Intelligences with Nature; The Souls, with the Quintessence, Nature, with Matter, as with a Vehicle.
4. The Intelligences are defined both to the power and knowledge: for they cannot operate any thing without the command of God.

1. Proposition

God operateth; by the communication of his Velle, or Decree, to the first matter of Creation; the first matter, to the Intelligence; the Intelligence, to the Soul; the Soul, to Nature; Nature, to Matter; doth communicate the Velle Dei.

1. Demonstration

God communicated his Decree of the Creation of Adam, to the first Matter; the first Matter, to the Determinate Intelligence; the Intelligence, to the Determinate Soul; the Soul, to Nature; Nature, to Matter.

These being concentrated by the Velle, or Decree of God, into one Microcosm, hence floweth the creation of Adam.

2. Demonstration

In the Generation of Eve, God communicated his Decree of her Generation to the first Matter; the first Matter, to the Intelligence of Adam; the Intelligence, to the Soul; the Soul, to the Fancy; the Fancy, to the Animal, Vital, and Natural Spirits.

The Animal, Vital, and Natural Spirits, being concentrated and fermented in the Spermatick Vesskials, by the Phantasma of the Fancy Sigilled upon them.

From the Spirits thus concentrated and fermented, by the Image of God in them; resulted the Generation of Eve. The Generation of our Savior was after this manner, as hath been demonstrated.

3. Demonstration

In the Conception of Christ, the Essence of God united with the humane Nature of Christ, by Concentration of the first matter of Creation, in humane Nature: Therefore Christ is Light and Life, the Light that illuminateth every one that cometh into the world; the Life that giveth Life, and reviveth all Mankind: from him we live, move, and have our being. The Universal Panacea, or Elixir, that cureth all by the water of Regeneration, and fire of the Spirit: The Philosophers Stone, who transmuteth the Signature of the Spirit of the Universe, and liberats the Image of God, or Spirit of Man from Darkness and Captivity, into the glorious light of liberty.

2. Proposition

Lucifer and his Concomitants desiring to be equal with God, united themselves with the first Matter or Image of God in the second, viz., Light, whereby they might have absolute power over Matters.

4. Demonstration

Lucifer and his Concomitants being in Fermentation, thorow the desire of Union with the first Matter, communicated the Signature thereof to Matter, by the Vihicle of Nature. Matter being thus fermented with the Signature, became pregnant; Matter being thus conceived, God therefore eclipsed the Conception, whereupon followed Abortion.

Lucifer and his Concomitants being eclipsed, in the Conception of the glorious light, Sigilled the circumference of Nature, viz. the Elementa Elementata, and the Principia Principiata, with the Signature of the desire of Dominion over another: Hence followeth contention and contrariety, transmutation of each into another, corruption and death.

Having thus Sigilled the Elementa Elementata, and Principia Principiata, they concentred and fermented them in the sight of Eve; whereby she saw the forms of all things, in a Glorious Figure: with the which aspect, her Fancy being fassinated, she was attracted. Her Fancy being thus attracted, with the Species of the object represented, communicated the Species thereof to the Soul, the Animal, Vital, and Natural Spirits, and consequently to the whole Body. The Union thereof was mediated by the Efflux and Reflux of the Celestial Body: by the Efflux to matter Sigilled, with the Signature of Envy, and emulation against God, and against his Image.

By the Reflux from Matter, thereby the Spirit of Man is more and more transmuted according to the Fermentation and Exaltation of the Fancy from Light to Darkness; from Union and Communion with God, into Union and Communion with the Spirit of the Universe.

Eve being thus fassinated, did fassinate Adam by Union of her Animal, Vital, and Natural Spirits, (transpiring and exhaling through the pores of the Body) being Sigilled with Adams Spirit: The Spirits being thus United, Sigilled the Spirits of Adam; the Spirits, the Fancy; the Fancy, the Soul: hence Diseases, Death, Damnation.

3. Proposition

The Primitive Origin of Diseases is the Union of the Spirit of Man with the Spirit of the World.

The Second Cause is the Signature of Emulation, Sigilled in the Humane Nature. As the Cause is two-fold, so the Cure.

First Cure is by Dissolution of the Union; The second is by Transmutation of the Signature.

5. Demonstration

The Union of the Spirit of God, is the Dissolution or Dis-union of the Spirit of the Universe: As the Degree of Union, so is the Degree of Dissolution; a total Union of the Spirit of Man with the Spirit of God, is a total Dissolution or Liberation from the Spirit of the Universe. A total Union is Glory and Heaven. The Multiplication of the Union is by the continual reflection of the Spirit of Man upon God in Christ.

The means are the Holy Scriptures, Faith, Love, Patience, Repentance, Contrition of Spirit, Humility, Self-denyal, Prayer in Spirit and Truth, Continence, Temperance.

The 2nd part of the Demonstration

Transmutation of the Signature is effected immediately by Prayer in Faith, working by Love.

Transmutation of the Signature is mediately by Signature, Sigils of Constellations, characters of Planets, and of Angels, Numbers, Words, &c. Concerning which I have written in a Book, called Lux e Tenebris, which I intend shortly to put to the Press; therefore I shall be Brief in this Treatise.

The Signatures are in Animals, Vegitables, Mettallick Bodies, and Mettals.

Amongst Animals Man hath the chiefest Signature in his Blood; Amongst Vegetables the Quintessence of Saffron; of the Berries of Juniper, of the Seeds of Rew (Juniper and Rew having the signature of the Cross) of the Quintessence of Cedar of Wine, &c.

Amongst Mettallick Bodies and Mettals preparations made out of the Minera of Mercury and Antimony, Venus, Luna, Sol, have the principallest signature.

Numbers have Efficacy and Energy

Instance he that hath the Number seven, in his Nativity; can by the signature thereof, cure diseases universally, if it be fortified and multiplied by a continual reflection upon God: with the which Signature I was dignified in my Nativity; and thereby have transmuted with admirable success, the Signature of the Kings Evil, Epilepsy, Podagra, &c. and have removed the occaissonal matter with Elixir and Balsam: with Elixars out of Mettallick Bodies, Mettals, and out of the Universal spirit incorporated and fixedin Corals, Pearls, Saltpeter, Vitriol, &c.

With Balsam made out of the mineral Sulphur, and out of vegetable Sulphur; viz. by the coagulation of the Oyl with the Volatile Salt: out of Animal Sulphur by putrefaction, seperation of the principles, and conjunction and union of them again.

Demonstrations and Preparations of Mettallick bodies and Metals, and of the Spirit of the Universe incorporated.

Take the King and the Queen and put them in the Wedlock bed; then after fourty dayes the Queen shall conceive with a Royal Child; (the conception being initiated) the Embrion is to be nourished with Virgins Milk untill the full perfection thereof.

Take Gold, and distill it seven times over the retort, with the menstruum mundi; the Gold being thus volatized by distillation, is to be sublimed with three parts of Mercury to one of Gold, until all the Gold be sublimed.

The Gold being thus sublimed with Mercury, then should it be calcined with a Philosophical calcination. The Mercury with the Gold, being thus calcined, then the bodies of both are pre-disposed for the Extraction of the tincture with the menstruum mundi. Hence ye shall have the medicine, whose Vertues and Properties will celebrate it self.

Take Mettallick Bodies, Mettals, and the Spirit of the Universe incorporated, and elevate them unto their Heaven; then circulate them until they have traced the seven sphears of the Planets, then reduce them into their Virgin Earth: whence you have a Medicine and Elixar (of each of the premised) curing all diseases Corolary, Mercury and Antimony being prepared according to their ordinary manner of preparation, are at the best exalted Poison, until they be perfectly fixed, which can be done by no means but by separating the impure from the pure; and by joyning and congealing the central Mercury with that which is of a homegeneous nature; according to these Axiomes, Natura natura letatur unitur, transmutat & multiplicat.

Demonstrations of the preparation of Balsums out of Sulphur of Minerals Vegetables and Animals.

Take Mineral Sulphur, and elevate it to its Heaven by the Separation of the impure from the Pure, with a fit medium; the superfluous Sulhpur being thus separated, ye may extract the tincture thereof with the Spirit of Wine.

Take Saffron, Juniper Berries, Seeds of Rew, Aloes, Cedar, and digest them in the menstruum of Alcalice volatized with essential Oyls according to the ordinary way; But if ye shall prepare them according to the Method that I have prescribed in the foresaid Book, you may do much better.

Demonstration of the Universal Panacaea, or of the Spirit of the Universe Incorporated in the second matter of Generation; by Axiomes and Conclusions.

Axiome 1. The Image of God is in Light as in its Vehicle.

Ax. 2. Light is the Secret matter of Generation.

Ax. 3. Virgine Earth is the second matter of Generation.

Ax. 4. The Image of God by the Vehicle of Light, is united and concentred in the Virgine Earth.

Ax. 5. Light the first matter is concentred and fixed in Virgine Earth, the second matter.

Ax 6. The Image of God, in the first matter of Generation, uniting univocally and homogenically with the spirit of man, (being liberated from the bondage of Elementa Elementata, of the Principia Principiata) doth increase and multiply it according to the degree of union.

Con. Virgine Earth is the subject matter; in which Light and Life is terminated and concentrated.

Con. The Light and Life in Virgine Earth, causeth Vegitation, Generation and Motion in all the products thereof.

Con. Virgine Earth being purified by exaltation and sublimation, from the circumferential and superficial impurity, is the universal Panaceaea that conserveth and multiplieth Light and Life in all its products.

Having demonstrated breifly the method and process of Creation Generation, of Origin of Causes, and of their Cure, I shall conclude with praise and glory to the IMMENSE LIGHT, in whom we live, move, and have our being.